Place the haddock in a pan with the milk and half the butter.
Bring to the boil, then poach for 10 minutes.
Remove the skin and any bones and flake the fish.
Cook the rice in plenty of boiling salted water for about 10 minutes, until just tender.
Chop two of the eggs.
Cut the other two in half, remove and sieve the yolks and chop the whites; set aside for garnish.
Melt the remaining butter in a pan and stir in the fish, rice and chopped eggs.
Heat gently for 5 minutes.
Transfer to a warmed serving dish and garnish with the sieved egg yolk, chopped egg white and chopped parsley.
Serve immediately.